4-7: Writing Systems of Linear Equations

Front

What is a linear equation?

Back

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept of a linear equation?

Back

Front

How can you determine if two lines are parallel?

Back

Front

What does it mean for two lines to be perpendicular?

Back

Front

How can you solve a system of linear equations graphically?

Back

To solve a system of linear equations graphically, plot both equations on the same graph. The point where they intersect is the solution to the system.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

What is a consistent system of equations?

Back

A consistent system of equations has at least one solution. This can be either one unique solution (intersecting lines) or infinitely many solutions (coincident lines).

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations has no solutions. This occurs when the lines are parallel and never intersect.